Second or foreign language (L2) learners’ development of interlanguage pragmatic (ILP) competence to understand and properly interpret utterances under certain social and cultural circumstances plays a pivotal role in the achievement of communicative competence. The current study was designed to explore the effects of synchronous computer-mediated communication (SCMC) and asynchronous computer-mediated communication (ACMC) course modules delivered through social media networks (SMN) on the development of the Iranian L2 learners’ comprehension of implicatures. The participants of the study were 90 English-as-a-foreign-language (EFL) undergraduate students attending three intact classes. The classes were randomly assigned to one control and two experimental (SCMC and ACMC) groups. An open-ended implicature comprehension test was used to assess students’ ILP development in this pretest-posttest comparison-group study. The control group received the traditional teacher-fronted instruction, and the S/ACMC groups received instruction via synchronous and asynchronous modules of SMNs for 4 months, respectively. Students’ attitudes towards the CMC-based courses were also sought. Split-plot ANOVA results indicated that both experimental groups developed significant ILP ability to comprehend and interpret L2 implicatures after the instruction; however, by comparison, the ACMC group improved more considerably. It is concluded that, first, comprehending L2 implicatures is not impervious to computer-mediated instruction and, second, different CMC affordances may result in differential ILP developmental effects in teaching L2 pragmatics. The findings can help L2 teachers decide how to use CMC affordances and SMN modules to raise L2 learners’ pragmatic awareness